guidance and control methods for formation flight by john deyst april 1, 2004 excerpted from the...
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Guidance and Control Methods for Formation Flight
by
John DeystApril 1, 2004
Excerpted from the Ph.D. Thesis Defense
of
SanghyukPark
November, 2003
Presentation Outline
• Background & Motivation
• Parent/Child UAV Project
• Guidance for Phase I
• Estimation
• Flight Test Results
• Summary
Why Formation Flight ?
• Aerial Refueling
• Fuel Efficiency
• UAV Landing on Shipboard / Humvee
If Rendezvous Large UAV + Small UAVs:
• Sustained Close-inSurveillance
by refueling small UAVs
• Retrieval of Small UAVs
A Possible Approach toFormation Flight Guidance
• Central generation of commanded flight paths
• Individual control of path following
Presentation Outline
• Background & Motivation
• Parent/Child UAV (PCUAV) Project
• Guidance for Phase I
• Estimation
• Flight Test Results
• Summary
PCUAV Project Objectives
• Guidance and control system development
• Flight tests for mid-air rendezvous of two small UAVs
• Maximum use of inexpensive (off-the-shelf) components
Approach & Challenges
• PHASE I
- MINI UAV approaches Parent to within 20 m from any initial position and flies in formation using stand-alone GPS
Challenges - Path planning
- Tight control/guidance on the desired trajectory for rendezvous & formation flight
• PHASE II
- Brings two UAVs even closer ~2 m
by adding more accurate sensor
Challenges -Accurate sensing/estimation & very tight control
•Higher Bandwidth (Agile) Vehicles Must Take on Challenging Tasks•Use Control Law Sophistication instead of Costly Instrumentation
Research Contributions
Theoretical Contributions
High accuracy control of small UAVs -position(2m), velocity (1m/s)
Autonomous rendezvous and formation flight of Child UAV with Parent UAV (Phase I)
Nonlinear lateral guidance logic for tightly tracking a given trajectory
Effective and simple, low-order attitudeestimation combining aircraft kinematics, GPS, and low quality inertial sensors
Autonomous control and guidance for docking of Child UAV with Parent UAV (Phase II)
Demonstration VehiclesRef. Master’s Theses of Francois Urbainand Jason Kepler
• Wingspan = 2.5 m
• Gross Weight = 10 kg
• GA-15 Airfoil
• .91 cu. in. O.S. Engine, Pusher Prop.
• Vertical fin (direct side force)
• Large area flaperons(direct lift)
• Wingspan = 4.5 m, Tailspan = 6.1 m
• Gross Weight = 20 kg
• NACA 2412 Airfoil
• Moki 2.10 cu. in. Engine (5 hp max)
• Outboard Horizontal Stabilizer (OHS)
→Open space behind, Aerodynamic efficiency
Avionics• PC/104 Computer Stack -CPU module, Analog Data module, Utility module• GPS : Marconi, Allstar GPS Receiver• Inertial Sensors -Crossbow 3-axis Accelerometer (MINI) -Tokin Ceramic Gyro (MINI) –Note : drift by 3~5 deg/min -Crossbow IMU (OHS)• Pitot Static Probe : hand-made with Omega, Pressure Sensor• Altitude Pressure Sensor (for high frequency estimation)• Communication : Maxstream, 9XStream Transceiver
: $ 2,200: $ 1,000
: $ 350: $ 150: $ 3,500: $ 75: $ 75: $ 200
200Avionics ~ Mini : $ 4,000 OHS : $ 7,500
Presentation Outline
• Background & Motivation
• Parent/Child UAV Project
• Guidance for Phase I
• Estimation
• Flight Test Results
• Summary
Phase I Flight PathRef. Master’s Thesis of Damien Jourdan
• Parent is maintained on circle
• Parent transmits its path to the
Mini, which generates a path plan
to follow the parent
1: Climb
2: Straight (synchronization)
3: Turn (R=250m)
4: Straight
5: Formation Flight
• Relative longitudinal position control
by Mini during 5
Previous Work on Outer-Loop Guidance
• Cross-track Error Guidance (typically PD controller)
Limitation Performance degrades on curved paths
• M. Niculescu(2001)
Limitation Flies straight line trajectories between waypoints
• Guidance Laws for Tactical Missiles -Line-of-sight guidance -Proportional Navigation-Pursuit guidance-Optimal linear guidance Limitation Cut corners on curved trajectories
New Guidance Logic for Trajectory Following
Select Reference Point
• On desired path
• At distance L in front of vehicle
Generate LateralAcceleration command:• Direction : serves to align V with L• Magnitude = centripetal acceleration necessary to follow the instantaneous circular segment defined by the two points and the velocity direction
Vehicle Dynamics
Mechanism of the Guidance Logic
Reference Point Selection
+
Acceleration Command
Convergence to Desired Path
Decomposition of the Bearing Angle ( η)
desired trajectory
anticipate curved pathFeed back heading error
Feed back displacement error
System Configuration
• A system block diagram is-
• Both the geometry and the guidance logic are nonlinear
• A small perturbation linear analysis can provide important insights
Geometric Calculation
Guidance Logic
Aircraft Dynamics
GPS/Inertial System
ReferenceTrajectory η
Aircraft Position
Linear Properties of Guidance Law
Assumptions• Aircaft is close to a desired straight line path
• Heading angle is close to path heading
Proportional +Derivative (PD) control
Linear Properties of Guidance Law (cont.)
The linearized guidance equation for lateral motion is
and a block diagram of the linearized system is-
Linear Properties of Guidance Law (cont.)
The system is linear, constant coefficient, and second order
Its characteristic equation can be written as
which yields
so the undamped natural frequency and damping ratio are
Linear Properties of Guidance Law (cont.)
For small perturbations about the desired trajectory
• The system is approximately linear and second order
• Its damping ratio is always.707
• The undamped natural frequency (bandwidth) is proportional to velocity (V) and inversely proportional to the trajectory reference point distance (L)
Thus, if the aircraft is traveling at 200 m/s and the desired system bandwidth is 0.5 rad/sec, then the trajectory reference point distance must be
Comparison -Straight LineFollowing
desired trajectory
PD Linear Control New Guidance Logic
Comparison –Curved Line Following
desired trajectory
PD,PID Linear Control New Guidance Logic
Comparison –Curved Line Following with Wind
desired trajectory
PD,PID Linear Control New Guidance Logic
Summary of the Lateral Guidance Logic
Superior performance of the nonlinear guidance logic comes from :
1.The feedback angle anticipates the future trajectory to be followed
2.Use of inertial speed in the computation of acceleration makes the system adaptive to changes in vehicle speed due to external disturbances such as wind
3.The nominal trajectory is a circular arc so the system doesn’t cut corners on curved trajectories
4.Small perturbation behavior is second order with a damping ratio of .707
5.The lateral displacement from the reference trajectory converges asymptotically to zero
Sensitivity to Bank Angle Biases
• Aircraft bank angle is used to generate lateral acceleration• Bank angle biases result in lateral acceleration biases• The guidance law will correct these accelerations but a trajectory
bias error will result
No integral control element
→Not robust to the bias in lateral acceleration
Simulation with 3 degree bank angle bias :~ 9 m steady cross-track error
Sensitivity to Bank Angle Biases (cont.)
• Assuming the bank angle bias is small the linear system can be used to understand its effect
• The bank angle bias produces a lateral acceleration bias
• The lateral acceleration bias produces a bias in lateral position
• GPS/Inertial information can be used to effectively eliminate lateral acceleration bias
Presentation Outline
• Background & Motivation
• Parent/Child UAV Project
• Guidance for Phase I
• Estimation
• Flight Test Results
• Summary
Previous Attitude Estimation Methods• Traditional AHRS with INS -Integration of rate gyros →Euler angle -Roll/Pitch correction by accelerometers (gravity aiding), Heading correction by c
ompass Drawback : requires high quality, low drift inertial sensors
• INS/GPS Integration Methods -Many integration architectures: uncoupled/loosely/tightly coupled -trade-off (cost, constraints, performance) Drawback : high cost, complexity
• Multi-Antenna GPS-Based Attitude Determination(Cohen, 1996) -Use multiple antenna (typically at least 3), carrier phase differences -The attitude solution can be combined with inertial sensors in complementary filt
er Drawback : multi-path, integer ambiguity, performance depends on baseline length
Previous Attitude Estimation Methods Using Aircraft Kinematics
Complementary filter with roll and raw gyrosSingle-Antenna GPS Based
Aircraft Attitude Determination
-Richard Kornfeld, Ph.D.(1999)
Drawback : sampling rate limit (GPS), typical filter time constant ~ 0.5 sec.
Drawback : biased estimate
Roll Rate Gyro
Roll angle estimate
Yaw Rate Gyro
Estimation of Bank Angle & Roll / Yaw Rate Gyro Biases
Kalman Filter Setup
Measurement Equation Filter Dynamics
φ: bank angle V: velocityαs: acceleration in sideways directionp: roll rate r: yaw rateVi,ωi: white noises
Contributions of Measurements on Estimates(Examples : Estimates of Bank Angle & Yaw-Rate Gyro Bias)
Bank Angle Estimate
low freq. : GPS acceleration
mid freq. : yaw rate gyro + GPS acceleration
high freq. : roll rate gyro
Yaw-Rate Gyro Bias Estimate
roll rate gyro doesn’t have effect
GPS acceleration, yaw gyro: 180 deg. phase diff.
for bank angle estimate for yaw-gyro bias estimate
Estimation of Pitch Rate Gyro Bias
ah :acceleration in height (vertifcal) directionV : velocityq : pich rateVi,ωi : white noises
Kalman Filter Setup
Measurement Equations Filter Dynamics
from GPS Kalman Filter
from Rate Gyro
Note: for turning with large bank angles, replace
Presentation Outline
• Background & Motivation
• Parent/Child UAV Project
• Guidance for Phase I
• Estimation
• Flight Test Results
• Summary
Flight Test Data : Rate Gyro Bias Estimation
flight trajectory
Flight Test Data : Longitudinal Control Phase I Controller
Error Mini
Altitude <1m for 90%
Air Speed <1m/s for 88%
Flight Time Percentages Within Error Bounds
Error OHS Parent
Altitude <2m for 97%
Air Speed <1m/s for 86%
Example: Mini
Flight Test Data -Lateral Trajectory Following Phase I Controller
Displacement Error (during on circle) : < 2 m for 75 %, < 3 m for 96 % of flight time
Displacement Error (after initial transition) : < 2 m for 78 %, < 3 m for 97 % of flight time
MINT OHS Parent
Flight Test Data –Phase IP: OHS Parent
M:Mini
Flight Test Data –Phase IRelative Position Difference during Formation Flight
During Formation Fight
Error < 2m for 86% of flight time
Error < 2m for 84% of flight time
Summary of Contributions
• Lateral Guidance Logic for Trajectory Following
•Tight Tracking for Arbitrary Curved Path Trajectories •Adaptive to Speed Changes due to Wind Disturbances
• Estimation using Aircraft Kinematics + GPS + Low Quality Gyros
•Simple & Low-Order •Provides a Means for Non-biased Lateral Acceleration Determination
• Trajectory Following for Two UAVs
•Implementation & Flight Demonstration of Guidance & Estimation Methods•Precise Control in the Presence of Wind Speed Disturbances ~ 5 m/s (> 20% of Flight Speed)
• Phase I Rendezvous Flight Demonstration
•Most precise Control of Relative Positions of Two UAVs Demonstrated To Date
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